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Excerpt Edition
This PDF is an excerpt from Chapter 2
of the Parametric Measurement Handbook.
The
Parametric Measurement
Handbook
Third Edition
March 2012
Chapter 2: Parametric Measurement Basics
"I often say that when you can measure what you are speaking about, and
express it in numbers, you know something about it ..."
"But when you cannot measure it, when you cannot express it in numbers, your
knowledge is of a meager and unsatisfactory kind; it may be the beginning of
knowledge, but you have scarcely, in your thoughts, advanced to the stage of
science, whatever the matter may be."
-- William Thomson (Lord Kelvin)
Measurement terminology
Before you can begin to collect measurement data you need to know basic
measurement terminology. In particular, understanding the precise meaning of
the terms accuracy, repeatability and resolution is essential to understanding
parametric test and the measurement capabilities of a parametric measurement
resource.
Accuracy and repeatability
Accuracy and repeatability are related but different quantities. Accuracy is the
degree of conformity of a measured or calculated quantity to its actual (true)
value. Repeatability (also known as precision) is the degree to which repeated
measurements or calculations show the same or similar results. Accuracy and
repeatability do not have any innate correlation. A measurement can have high
accuracy and high repeatability, high accuracy and low repeatability, low accu-
racy and high repeatability, or both low accuracy and low repeatability.
The visual analogy that is often used to explain these terms is a bull's-eye target.
A group of points that are close to the center of a target but spaced far apart
from one another (as shown below) have high accuracy but low repeatability.
High accuracy, low repeatability
Figure 2.1. High accuracy and low repeatability.
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A group of points that are far from the center of a target but spaced close
together (as shown below) have low accuracy but high repeatability.
Low accuracy, high repeatability
Figure 2.2. Low accuracy and high repeatability.
The analogies for the two other cases should be fairly obvious. For production
parametric test, repeatability is usually more important than absolute accuracy.
This is because parametric test is concerned with monitoring trends, which
makes having highly repeatable measurements extremely important.
Resolution
For parametric test, resolution is what allows us to gauge accuracy and
repeatability. In this sense it is the most important specification for parametric
test. Resolution is the lowest resolvable quantity of data that an instrument
can accurately measure. The easiest way to think about this is in terms of an
analog-to-digital converter (ADC) circuit. The figure below shows a simplified
version of an ADC:
Clock
Analog
+
input Control
Up/down counter
-
D/A converter Digital output
Figure 2.3. Simplified analog-to-digital converter (ADC) circuit.
15
As this illustrates, the number of bits available to the digital-to-analog converter
(DAC) will determine the fineness of the measurement detail that can be distin-
guished, which is the resolution. For example, a resolution of 20 bits represents
the ability to distinguish one part in 220 or 1,048,576 (basically one part in a
million).
To express the measurement resolution in terms of current or voltage, you need
to know the measurement range in which you are operating. For example, in a 5 V
measurement range the ADC measures from